Question : In triangle ABC, $\angle$ABC = 15°. D is a point on BC such that AD = BD. What is the measure of $\angle$ADC (in degrees)?
Option 1: 15
Option 2: 30
Option 3: 45
Option 4: 60
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Correct Answer: 30
Solution :
Given: In triangle ABC, $\angle$ABC = 15°.
D is a point on BC such that AD = BD.
Given that AD = BD. Then, $\angle$ABD = $\angle$BAD = 15°
Now, in $\triangle$ABD
⇒ $\angle$ABD + $\angle$BAD + $\angle$ADB = 180°
⇒ $\angle$ADB = 180° – 15° – 15°
⇒ $\angle$ADB = 150°
We know that, $\angle$ADB + $\angle$ADC = 180°
⇒ $\angle$ADC = 180° – 150°
⇒ $\angle$ADC = 30°
Hence, the correct answer is 30.
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